Euclidean Rings

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Description

The cardinality of the set of units, and of the set of equivalence classes of primes in non-trivial Euclidean domains is discussed with reference to the categories "finite" and "infinite." It is shown that no Euclidean domains exist for which both of these sets are finite. The other three combinations are possible and examples are given. For the more general Euclidean rings, the first combination is possible and examples are likewise given. Prime factorization is also discussed in both Euclidean rings and Euclidean domains. For Euclidean rings, an alternative definition of prime elements in terms of associates is compared and ... continued below

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iv, 32 leaves

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Fecke, Ralph Michael May 1974.

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  • Fecke, Ralph Michael

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The cardinality of the set of units, and of the set of equivalence classes of primes in non-trivial Euclidean domains is discussed with reference to the categories "finite" and "infinite." It is shown that no Euclidean domains exist for which both of these sets are finite. The other three combinations are possible and examples are given. For the more general Euclidean rings, the first combination is possible and examples are likewise given. Prime factorization is also discussed in both Euclidean rings and Euclidean domains. For Euclidean rings, an alternative definition of prime elements in terms of associates is compared and contrasted to the usual definitions.

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iv, 32 leaves

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  • May 1974

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  • June 24, 2015, 9:39 a.m.

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  • Sept. 26, 2016, 2:14 p.m.

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Fecke, Ralph Michael. Euclidean Rings, thesis, May 1974; Denton, Texas. (digital.library.unt.edu/ark:/67531/metadc663654/: accessed November 14, 2018), University of North Texas Libraries, Digital Library, digital.library.unt.edu; .